This paper proposes an analytical method to investigate the out-of-plane vibration of thin-walled curved beams under a moving mass. This method comprehensively considers the warping stiffness, shear deformation, and rotatory inertia, as well as the inertia force caused by moving mass and damping. The Fourier sine integral transform and Laplace-Carson integral transform are used to decouple the system of equations for out-of-plane vibration of the thin-walled curved beam under a moving mass. Two dynamic response expressions in two directions involving vertical and torsional responses are easily obtained after using their inverse transforms. Numerical results demonstrate a strong agreement between the outcomes obtained from the proposed expressions and those obtained using numerical methods in existing literature. Furthermore, the effects of variables such as slenderness ratio, the center angle, velocity of the moving mass and eccentricity on the dynamic response of the thin-walled curved beam are discussed. For beams with small cross-sectional shear correction factor and slenderness ratio, ignoring the shear deformation, rotatory inertia, and warping stiffness of the beam can cause obvious errors for the natural frequency of the beam. Moreover, when the speed and mass of the moving load are large, it is necessary to consider the inertial force caused by the mass for studying the out-of-plane vibration of the thin-walled curved beam. The influence of shear deformation is less affected by the velocity and mass velocity of moving loads, and primarily depends on the structural characteristics of the curved beam itself. For beams of the same length, shear deformation becomes more pronounced with increasing radius of curvature.

中文翻译：

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运动质量作用下单对称截面Timoshenko薄壁曲梁面外振动分析方法


本文提出了一种研究运动质量下薄壁曲梁面外振动的分析方法。该方法综合考虑了翘曲刚度、剪切变形和转动惯量，以及运动质量和阻尼引起的惯性力。利用傅立叶正弦积分变换和拉普拉斯-卡森积分变换对移动质量下薄壁曲梁面外振动方程组进行解耦。使用它们的逆变换后，很容易获得涉及垂直和扭转响应的两个方向上的两个动态响应表达式。数值结果表明，从所提出的表达式获得的结果与使用现有文献中的数值方法获得的结果之间有很强的一致性。此外，还讨论了长细比、中心角、运动质量速度和偏心率等变量对薄壁曲梁动态响应的影响。对于截面剪切修正系数和长细比较小的梁，忽略梁的剪切变形、转动惯量和翘曲刚度会导致梁的固有频率产生明显的误差。而且，当移动载荷的速度和质量较大时，研究薄壁曲梁的面外振动需要考虑质量引起的惯性力。剪切变形的影响受移动载荷的速度和质量速度影响较小，主要取决于曲梁本身的结构特性。对于相同长度的梁，随着曲率半径的增加，剪切变形变得更加明显。